Harder--Narasimhan mass

The mass m_σ(E) of an object with respect to a stability condition: the sum of the norms of the central charges of its Harder--Narasimhan factors.

Placement

Mass is a sibling of Metric/, not a child of it. It is an invariant of an object and a stability condition, and its consumers are not only the distance construction: the mass--Hom estimates under StabilityCondition/MassHom/ use mass without using the metric, and dynamical constructions do the same. That independent consumer is what justifies the separate root; the metric construction is downstream and imports this API.

The Euclidean content of the subadditivity proof does not live here. The polygonal-path carrier, the real continuous linear functionals on ℂ and the perimeter comparison are neutral planar geometry and own DerivedAlgGeo/Analysis/Convex/ComplexPolygonalPath/; what stays below Subadditivity/ is the Harder--Narasimhan reading of those statements. MO1.13 (#1324).